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We study the spreading of renewable power fluctuations through grids with Ohmic losses on the lines. By formulating a network adapted linear response theory, we find that vulnerability patterns are linked to the left Laplacian eigenvectors…
The problem of robustly reconstructing a large number from its erroneous remainders with respect to several moduli, namely the robust remaindering problem, may occur in many applications including phase unwrapping, frequency detection from…
Robustness to adversarial attacks is typically evaluated with adversarial accuracy. While essential, this metric does not capture all aspects of robustness and in particular leaves out the question of how many perturbations can be found for…
We generalize our recent results for the boundary and interface charges in one-dimensional single-channel continuum [Phys. Rev. B 104, 155409 (2021)] and multichannel tight-binding [Phys. Rev. B 104, 125447 (2021)] models to the realm of…
Barrett et al studied resistance labels of electrical circuits whose underlying graphs when embedded in the Cartesian plane has the form of an $n$-grid, $n$ rows of upright triangles. Proofs in Barrett introduced a row-reduction algorithm…
In an alternating-current network, each edge has a complex "conductance" with positive real part. The response map is the linear map from the vector of voltages at a subset of "boundary nodes" to the vector of currents flowing into the…
We study Turing bifurcations on one-dimensional random ring networks where the probability of a connection between two nodes depends on the distance between the two nodes. Our approach uses the theory of graphons to approximate the graph…
The effectiveness of shortcut/skip-connection has been widely verified, which inspires massive explorations on neural architecture design. This work attempts to find an effective way to design new network architectures. It is discovered…
We study the corner-to-corner resistance of an M x N resistor network with resistors r and s in the two spatial directions, and obtain an asymptotic expansion of its exact expression for large M and N. For M = N, r = s =1, our result is…
Optical routers are fundamental to photonic systems, but their performance is often limited by unwanted reflections and constrained functionalities. Existing design strategies generally lack complete control over reflectionless pathways and…
Bayesian methods are often optimal, yet increasing pressure for fast computations, especially with streaming data, brings renewed interest in faster, possibly sub-optimal, solutions. The extent to which these algorithms approximate Bayesian…
We develop an algorithm for reconstruction of elastic strain fields from their Longitudinal Ray Transform (LRT) in either two or three dimensions. In general, the LRT only determines the solenoidal part of a symmetric tensor field, but…
This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower…
We study algorithms for the fast computation of modular inverses. Newton-Raphson iteration over $p$-adic numbers gives a recurrence relation computing modular inverse modulo $p^m$, that is logarithmic in $m$. We solve the recurrence to…
We identify a trade-off between robustness and accuracy that serves as a guiding principle in the design of defenses against adversarial examples. Although this problem has been widely studied empirically, much remains unknown concerning…
We study the transfer of adversarial robustness of deep neural networks between different perturbation types. While most work on adversarial examples has focused on $L_\infty$ and $L_2$-bounded perturbations, these do not capture all types…
This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary,…
Deep neural networks are easily misled by adversarial examples. Although lots of defense methods are proposed, many of them are demonstrated to lose effectiveness when against properly performed adaptive attacks. How to evaluate the…
The total effective resistance, also called the Kirchhoff index, provides a robustness measure for a graph $G$. We consider two optimization problems of adding $k$ new edges to $G$ such that the resulting graph has minimal total effective…
This paper studies the difficulty of discriminating between an arbitrary quantum channel and a "replacer" channel that discards its input and replaces it with a fixed state. We show that, in this particular setting, the most general…